To find the coordinates of the reflection of point P (3, 10) across the line y = 1, we first need to understand how reflection works in relation to a line.
The line y = 1 is a horizontal line that runs along the y-axis at the y-coordinate of 1. The distance from point P to the line y = 1 can be calculated by subtracting the y-coordinate of the line from the y-coordinate of point P:
- Distance = y-coordinate of P – y-coordinate of the line = 10 – 1 = 9
When we reflect point P across the line y = 1, we will move the same distance below the line. Thus, we subtract the distance from the line:
- New y-coordinate = y-coordinate of the line – Distance = 1 – 9 = -8
Since the x-coordinate remains unchanged during a reflection across a horizontal line, the x-coordinate of the reflection will still be 3.
Therefore, the coordinates of the reflection of point P (3, 10) across the line y = 1 are (3, -8).